The electric potential V at a point in space equals zero. Which of the following must be true at that point?
AThe electric field is also zero
BNo net charge exists anywhere in the surroundings
CNo net work is needed to bring a test charge to that point from infinity
DPositive charges placed there will experience no force
V = 0 means U = qV = 0 for any test charge, so no net work is done moving it from infinity (where V is also defined as zero) to that point. The electric field at a point is E = −∇V; a field requires a *gradient* (slope) of potential, not a nonzero value. A region can have V = 0 with a strong field if the potential is changing rapidly there — this is the most important misconception about potential.
Question 2 True / False
The electric potential is higher at a point closer to a positive point charge than at a point farther away from the same charge.
TTrue
FFalse
Answer: True
For a positive charge Q, V = kQ/r. Since k > 0 and Q > 0, V decreases as r increases — so points closer to the charge have higher potential. This is consistent with the fact that positive test charges naturally accelerate from high to low potential (away from the positive source), just as objects fall from high to low gravitational potential.
Question 3 Short Answer
Why is electric potential (a scalar) typically easier to use than electric field (a vector) when computing the effect of multiple point charges?
Think about your answer, then reveal below.
Model answer: Potential obeys scalar superposition: the total potential at a point is the algebraic sum V = kQ₁/r₁ + kQ₂/r₂ + ... with no direction to track. Electric field requires vector addition — you must resolve each contribution into components and add them separately. Once total V is known, the field can be recovered from E = −∇V if needed.
This computational advantage is the main reason electric potential is introduced rather than working purely with fields. The strategy of 'find V first, then find E' solves many problems with far less algebra than direct vector field superposition.